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By regularly practicing RD Sharma Class 12th Exercise 17.3, understudies will be severe with the thoughts given in the Class 12 RD Sharma textbook. Be that as it may, it is nearly impossible to be skilled at maths who thought proper practice. The Rd Sharma class 12th exercise 17.3 will help students to learn and practice at home so that they have the chance to improve their skills to score well in boards and JEE mains.
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Maxima and Minima excercise 17.3 question 1 (i)
Answer:Maxima and Minima excercise 17.3 question 1 (ii)
Answer:
point of local maxima is 1 & its max. value is 19 & point of local minima is 3 & its value is 15.
Hint:
First find critical values of f(x) by solving f'(x) =0 then find f''(x).
If then is point of local minima.
If then is point of local maxima .
where & are critical points.
Put and in f(x) to get minimum value & maximum value.
Given:
Explanation:
We have,
To find maxima and minima.
At x = 3,
f’’(3) = 6(3)-12
=6>0
So, x = 3 is point of local minima
At x = 1,
f’’(1) = 6(1)-12
=-6<0
So, x = 1 is point of local maxima
Now, local maximum value at x= 1 is
And local min. value at x=3 is
Thus, point of local maxima is 1 & its max. value is 19 & point of local minima is 3 & its value is 15.
Maxima and Minima exercise 17.3 question 1 (iv)
Answer:
Point of local maxima is 2 and it’s local maximum value isAnswer:
Point of local minima value is x=-1 and it’s local minimum value is
Hint:
First find critical values of f(x) by solving f'(x) =0 then find f''(x).
First find critical values of f(x) by solving f'(x) =0 then find f''(x).
If then is point of local minima.
If then is point of local maxima .
where & are critical points.
Put and in f(x) to get minimum value & maximum value.
Given:
Explanation:
We have,
Now, for maxima & minima, f’(x)=0
at x=-1,
X = -1 is point of local minima.
So, local min. value at x= 1 is
Thus, point of local minima is -1 & its min value is
Maxima and Minima Excercise 17.3 question 1 (vii)
Answer:
Point of local minima value is and it’s local minimum value is
Hint:
First find critical values of f(x) by solving f'(x) =0 then find f''(x).
If then is point of local minima.
If then is point of local maxima .
where & are critical points.
Put and in f(x) to get minimum value & maximum value.
Given:
Explanation:
we have ,
For maxima & minima, f’(x)=0
At x=
So , is a point of local minima
Now at
Thus, point of local minima is & its value is
Maxima and Minima exercise 17.3 question 1 (viii)
Answer:Point of local maxima value is and it’s local maximum value is Also point of local minima is a and it’s local minimum value is 0.
Hint:
First find critical values of f(x) by solving f'(x) =0 then find f''(x).
If then is point of local minima.
If then is point of local maxima .
where & are critical points.
Put and in f(x) to get minimum value & maximum value.
Given:
Explanation:
We have,
For maxima and minima f’(x) =0
At x= a,
So, x=a is point of local minima
Now at x=a,
Also, at
Thus, point of local maxima is & its max. value is & point of local minima is a & its value is 0.
Maxima and Minima excercise 17.3 question 1 (x)
Answer:Maxima and minima exercise 17.3 question 1 (xi)
Answer:
x=1 is a point of local maxima and its maximum value is 1 and x=-1 is a point of local minima and its minimum value is -1.So x=1 is local maxima and its maximum value f(1)=1
So , x = 1 is a point of local maxima and its minimum value f(-1)=-1
Maxima and Minima Excercise 17.3 question 1 (xii)
Answer:So is a point of local maxima
The local maximum value at f(x)
Maxima and Minima excercise 17.3 question 2 (iii)
Answer:Thus this test is fail as x=1 is point of inflexion
when
So , x = -1 is a point of local minimum
When
So, x=-1/5 is the point of local maximum
Maxima and Minima exercise 17.3 question 5
Answer:Maxima and Minima exercise 17.3 question 6
Answer:Maxima and Minima exercise 17.3 question 7
Answer:
Hint:
Put,
Given:
Explanation:
Differentiating f(x) with respect to x
Put and and as they are the extremum values hence
Answer:
Hence proved.
Hint:
Put,
Given:
Explanation:
Differentiating fx with respect to x
Differentiating f’(x) with respect to x ,
So, is a point local maxima.
Rd Sharma Class 12th exercise 17.3 is an essential part of the RD Sharma solutions for maths. The Class 12 RD Sharma chapter 17 exercise 17.3 solution will contain an important chapter of the NCERT maths book that needs to be studied well. RD Sharma Class 12 Solutions Maxima and Minima Ex 17.3 is going to be based on the chapter Maxima and minima.
Rd Sharma class 12-chapter 17 exercises 17.3 answers that are basic and simple. It will help students learn all formulae well and become skilled at the subject in general. RD Sharma class 12 solutions ex 17.3 has around 21 inquiries.
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It's significantly suggested that class 12 RD Sharma chapter 17 exercise 17.3 solution should be used by students to check their answers and mark themselves to record their performance.
There are 21 answers corresponding to the NCERT book in Class 12 RD Sharma chapter 17 exercise 17.3 solutions
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